Unitary Invertible Graphs of Finite Rings

Let R be a finite commutative ring with unity. In this paper, we consider set of additive and mutual additive inverses of group units of R and obtain interrelations between them. In general φ(Zn) is even, however we demonstrate that φ(R) is odd for any finite commutative ring with unity of Char(R) ≠...

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Main Authors:	Chalapathi Tekuri, Sajana Shaik
Format:	Article
Language:	English
Published:	Sciendo 2021-05-01
Series:	Discussiones Mathematicae - General Algebra and Applications
Subjects:	finite commutative rings additive and mutual additive inverses euler-function unitary invertible graphs basic and non-basic triangles 11g15 11t30 05c30
Online Access:	https://doi.org/10.7151/dmgaa.1350

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spelling	doaj-40ef50fc031a41b086874e04bb6b12e32021-09-05T17:19:43ZengSciendoDiscussiones Mathematicae - General Algebra and Applications2084-03732021-05-0141119520810.7151/dmgaa.1350Unitary Invertible Graphs of Finite RingsChalapathi Tekuri0Sajana Shaik1Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati, A.P., IndiaDepartment of Mathematics, P.R. Govt. Degree College (A), Kakinada, A.P., IndiaLet R be a finite commutative ring with unity. In this paper, we consider set of additive and mutual additive inverses of group units of R and obtain interrelations between them. In general φ(Zn) is even, however we demonstrate that φ(R) is odd for any finite commutative ring with unity of Char(R) ≠ 2. Further, we present unitary invertible graph related with self and mutual additive inverses of group units. At long last, we establish a formula for counting the total number of basic and non-basic triangles in the unitary invertible graph.https://doi.org/10.7151/dmgaa.1350finite commutative ringsadditive and mutual additive inverseseuler-functionunitary invertible graphsbasic and non-basic triangles11g1511t3005c30
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Chalapathi Tekuri Sajana Shaik
spellingShingle	Chalapathi Tekuri Sajana Shaik Unitary Invertible Graphs of Finite Rings Discussiones Mathematicae - General Algebra and Applications finite commutative rings additive and mutual additive inverses euler-function unitary invertible graphs basic and non-basic triangles 11g15 11t30 05c30
author_facet	Chalapathi Tekuri Sajana Shaik
author_sort	Chalapathi Tekuri
title	Unitary Invertible Graphs of Finite Rings
title_short	Unitary Invertible Graphs of Finite Rings
title_full	Unitary Invertible Graphs of Finite Rings
title_fullStr	Unitary Invertible Graphs of Finite Rings
title_full_unstemmed	Unitary Invertible Graphs of Finite Rings
title_sort	unitary invertible graphs of finite rings
publisher	Sciendo
series	Discussiones Mathematicae - General Algebra and Applications
issn	2084-0373
publishDate	2021-05-01
description	Let R be a finite commutative ring with unity. In this paper, we consider set of additive and mutual additive inverses of group units of R and obtain interrelations between them. In general φ(Zn) is even, however we demonstrate that φ(R) is odd for any finite commutative ring with unity of Char(R) ≠ 2. Further, we present unitary invertible graph related with self and mutual additive inverses of group units. At long last, we establish a formula for counting the total number of basic and non-basic triangles in the unitary invertible graph.
topic	finite commutative rings additive and mutual additive inverses euler-function unitary invertible graphs basic and non-basic triangles 11g15 11t30 05c30
url	https://doi.org/10.7151/dmgaa.1350
work_keys_str_mv	AT chalapathitekuri unitaryinvertiblegraphsoffiniterings AT sajanashaik unitaryinvertiblegraphsoffiniterings
_version_	1717786570621190144

Unitary Invertible Graphs of Finite Rings

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